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Their proposed blackholes are small - some of their calculations use 4 × 10^11 grams [440.924 tons ~ comparable to Empire State Building which weights about 300.000 tons].

The radiation involved means that you probably couldn't shield a human well enough to be close enough to one of these black holes to feel gravity. Not to mention tidal forces.

I meant, how do you stop the black hole from hitting the spaceship, moving around, falling out the back, etc?

They touch on this briefly at the top of page 11: "The most optimistic approach is to solve requirements 2 [accelerate the black hole to keep it with the ship] and 3 [feeding the black hole with matter so that it doesn't evaporate] together by attaching particle beams to the body of the ship behind the BH and beaming in matter. This would both accelerate the SBH, since BHs “move when you push them” (see [3] p270), and add mass to the SBH, extending the lifetime."

The engineering details are left as an exercise for the reader :-)